Discrt Dynamics in Natur and Socity, Articl ID 949475, 8 pags http://dx.doi.org/10.1155/2014/949475 Rsarch Articl Modling th Prcptions and Prfrncs of Pdstrians on Crossing Facilitis Hongwi Guo, 1 Fachng Zhao, 1 Wuhong Wang, 1 Yanlong Zhou, 1 Yuji Zhang, 1 and Grt Wts 2 1 Dpartmnt of Transportation Enginring, Bijing Institut of Tchnology, Bijing 100081, China 2 Transportation Rsarch Institut (IMOB), Hasslt Univrsity, Wtnschapspark 5 bus 6, 3590 Dipnbk, Blgium Corrspondnc should b addrssd to Wuhong Wang; wangwuhong@bit.du.cn Rcivd 17 Novmbr 2013; Accptd 16 January 2014; Publishd 6 March 2014 Acadmic Editor: Huimin Niu Copyright 2014 Hongwi Guo t al. This is an opn accss articl distributd undr th Crativ Commons Attribution Licns, which prmits unrstrictd us, distribution, and rproduction in any mdium, providd th original work is proprly citd. Pdstrian s strt-crossing bhaviour has a significant ffct on traffic prformanc and safty. Th crossing bhaviour is dtrmind by human factors and nvironmntal factors. Aiming at xamining th pdstrian prcptions toward crossing facilitis and prfrncs for crossing locations, an obsrvational study of pdstrian crossing bhaviour at urban strt is conductd. Th prcptions and prfrncs of pdstrians ar collctd using statd prfrnc tchniqu. A spcific qustionnair is dsignd to conduct th statd prfrnc survy. A multinomial logit modl is proposd to dscrib th prcptions and prfrncs of pdstrians on crossing facilitis and locations. Th snsitivity analysis is prformd to discuss th influnc of various factors on crossing bhaviour. Thn th rlationship btwn crossing locations and crossing distancs is analyzd by a nw proposd mthod. With th thortical analysis, th nginring solutions considring pdstrian bhaviour ar suggstd. Th rsults ar hlpful to dsign human-cntrd crossing facilitis in urban traffic. 1. Introduction Pdstrians traffic bhaviour at urban ntwork includs walk along strts and cross strts. Onc pdstrians want to cross strts, it is invitabl that thy will conflict with motor vhicls. Traffic accidnts that involvd pdstrians and cyclists hav bcom a critical safty problm all ovr th world [1]. In a dvloping country, lik China, with larg population and wak infrastructur, pdstrians oftn bcom a rason for traffic congstion and traffic accidnts. To dal with pdstrian traffic problms, various crossing facilitis ar dsignd to assist pdstrian in crossing safly, for xampl, crosswalk (signalizd and unsignalizd), pdstrian ovrpass, and pdstrian undrpass at intrsction or midblock. With crossing facilitis, pdstrians ar sparatd from motor vhicls tmporally or spatially. Unfortunatly, pdstrians crossing bhaviour is strongly rlatd to human factors. Thus pdstrians may cross illgally rathr than using crossing facilitis. Th subjctivity and randomnss mak pdstrian bhaviour complicatd and also ncourag traffic nginrs to pay mor attntion to pdstrian traffic. Th rsarch on pdstrian charactristics is th basic and important part for traffic nginring. Fruin [2] publishd th monograph Pdstrian Planning and Dsign and it is rgardd as a foundation for pdstrian rsarch. Thn som particular rsarchs includd studis for bhaviour, psychology, safty, and simulation. Mohammd [3] valuatd pdstrian crossing spd in Jordan and valuatd th ffct of ag, gndr, and distanc crossd (strt width). Lam t al. [4] studid th rlationship btwn walking spd and pdstrian flow undr various flow conditions and th ffcts of bidirctional pdstrian flow on signalizd crosswalks in Hong Kong. Sisiopiku and Akin [5] prsntd findings from an obsrvational study of pdstrian bhaviour at various urban crosswalks in a dividd urban strt nar univrsity campus. Pdstrian lvl-of-srvic assssmnt modls wr introducd by diffrnt mthods undr various traffic conditions, and standards for ach lvl wr stimatd [6, 7]. Pdstrianbhaviourisvrycomplxandasilyinfluncd by nvironmntal dsigns and urban forms. A propr dsign of facilitis can ncourag walking without compromising safty and convninc [8, 9]. Th waiting tim
2 Discrt Dynamics in Natur and Socity Zon 1 Zon 2 Zon 3 Dstination Crosswalk Crossovr Origin Zon 4 Zon 5 Zon 6 Figur 1: Illustration of crossing rout. and crossing distanc (distanc btwn trip dstination and actual crossing location) ar th mainly xtrnal factors which would lad to unsaf crossing. Th nd to hurry or th dsir to kp moving along th shortcut is th main subjctiv rason bhind th lack of complianc with pdstrian signals or crossing facilitis. Pdstrian violation can b considrd as th invitabl outcom of th contradiction btwn xtrnal factors and human factors. Li [10] and Lambrianidou t al. [11] gav various rports about pdstrians bhaviour influncd by tim and distanc. Guo t al. [12, 13] analysd th waiting bhaviour during th strt crossing by using th rliability thory and indicatd th violation risk quantitativly with th incrasing waiting tim. Chu t al. [14] usd data obtaind from pdstrians statd crossing prfrnc and xplaind th statd prfrnc with th strt nvironmnt within th framwork of disaggrgat modls. Yannis t al. [15] improvd Chu s modl to valuat accidnt risk along a trip in rlation to th stimatd crossing bhaviourofpdstrians.nassiriandsajd[16]valuatdand idntifid th ffctiv paramtrs in pdstrian s dcisionmaking procss basd upon vhicl spd and hadway on multilan strts by using logit modl. It coms to a conclusion that a sris of studis hav providd insight into svral aspcts of pdstrian crossing bhaviour. Compard with th rsarchs about pdstrian accidnt analysis and safty valuation, th rsarchs about th prfrncs and prcptions of pdstrians on crossing facilitis and crossing locations ar limitd. Whil crossing a strt, th crossing facilitis and crossing locations play an important rol. Th xistnc of crossing facilitis is to nsur safty and assist accssibility. Howvr, som pdstrians do not lik using crossing facilitis and vn cross strt illgally bcaus thy do not think th facilitis can mt thir dmands. This papr aims at valuating pdstrian prfrncs for commonly ncountrd crossing facilitis and analysing pdstrian crossing locations in diffrnt conditions. To achiv such objctiv, a multinomial logit modl for pdstrian crossing bhaviour is proposd to analys th probability distribution of utilitis for various crossing facilitis. With th valuatd modl, pdstrian crossing locations ar xamind in various assumd traffic conditions so as to xplor th rasons bhind th crossing bhaviour. This papr hops to giv a bttr undrstanding of pdstrian crossing bhaviour. Th papr is organizd as follows. Sction 2 introducs th mthodology including discrt choic modl and data collction. Sction 3 dscribs th modl dmonstration and stimation. Sction 4 discussd pdstrian crossing bhaviour undr various influntial factors. Sction5 prsnts som nginring improvmnt for pdstrian facilitis considring th crossing bhaviour. Sction 6 prsnts som conclusions from this study and a tntativ plan for futur work. 2. Mthodology 2.1. Analysis of Pdstrian Crossing Bhaviour. As mntiond abov, pdstrian crossing bhaviour is strongly rlatd to human factors and traffic circumstancs. Pdstrians dcision making about whr to cross or whn to cross can b dscribd as th procss of prcption-judgmnt-dcisionaction. Gnrally, crossing dcision is influncd by charactristics of th trip (.g., th origin and dstination and th complxity and th lngth of th rout), charactristics of th infrastructur (.g., th typ of pdstrian facility, road gomtry, and traffic conditions), and individual charactristics (.g., ag and gndr and safty awarnss). Th crossing bhaviour shall thrfor rflct th combind assssmnt of th abov charactristics undr all sorts of conditions. In accordanc with human natur, crossing bhaviour xhibits significant subjctivity and randomnss. Thrfor, pdstrian crossing bhaviour may bcom risk-taking action and lad to conflicts with motor vhicls. Th procss of strt crossing can b xplaind by th utility maximization thory that pdstrians want to choos th most satisfactory facilitis and locations to cross th strt. As a rsult, pdstrians gt th maximum utility. It would b rasonabl to assum that pdstrians most satisfactory dcisions ar dpndnt on th location and th typ of crossing facility. For xampl, as shown in Figur 1,thrar two crossing facilitis in th ara. If a pdstrian s origin is in zon 5 and th dstination is in zon 2, thr ar thr potntial routs to cross th strt. Th first rout is to us
Discrt Dynamics in Natur and Socity 3 th crosswalk, th scond rout is to us th ovrpass, and th third rout is to cross at any location. Thrfor th xistnc of crossing facility may chang pdstrians crossing bhaviour and also induc traffic violation bcaus pdstrians cannot cross th strt at th dsird location. 2.2. Discrt Choic Modl Framwork. Th utilitarian approach of microconomic concpts is mployd and th discrt choic modl framwork is adoptd to dscrib crossing bhaviour. Th discrt choic modl is on of th most important modls for th rsarch on traffic bhaviour and is widly usd in transportation prdictions [17]. According to th stochastic utility modl, various altrnativs hav utilitis which will influnc th choic. In th bhaviour of facility choic, th altrnativ i (i.., th crossing facility i) within st of all lmntal altrnativs A I ; th utility function U in of facility i slctd by pdstrian n consists of an obsrvabl utility componnt V in and th unobsrvabl random componnt ε in.thutilitycanbdfindas U in =V in +ε in i A I ; i=1,...,i; n=1,...,n. (1) Assuming that ach pdstrian is th dcision makr of him/hrslf, th slction critrion is to maximiz th utility. In th stochastic utility modl, th probability to choos crossing facility n is P in = Prob (U in max U kn ;i=k,k A I ) = Prob (V in +ε in max (V kn +ε kn )), whr P in is th probability of crossing facility i slctd by pdstrian n, U kn is th utility function of othr altrnativs in choic st A I xcluding th altrnativ i,andprob( )isth probability function. Oprational modls ar basd on spcific assumptions about th distribution of ε in. Assuming i.i.d. xtrm valu distributions lad to th multinomial logit (MNL) modl, which has bn vry succssful du to its computational and analytical tractability. Th MNL modl for th slction bhaviour of pdstrian is dfind as P in = (2) xp (V in ) j AI xp (V jn ). (3) 2.3. Data Collction. Data collction was takn in spcific ara with mor than two typs of crossing facilitis. Th spacing btwn two facilitis was within 300 mtrs. Morovr, thr wr larg pdstrians to cross th strt. Th survy ara was dividd into 6 zons (or 8 zons) so that th pdstrians origins and dstinations can b rcordd accuratly. Finally, th Zhongguancun Strt and Xidan Strt in Bijing wr chosn as survy aras. Th data collction containd fild survy and qustionnair survy. Th fild survy obtaind th information about pdstrians crossing bhaviour. Th fild survy was conductd by obsrvrs at th appointd sit and it containd two aspcts: (a) to obsrv th crossing locations of pdstrians who had participatd in th qustionnair survy and (b) to obsrv and rcord th amounts of pdstrians usd crossing facilitis. Qustionnair survy was conductd to collct statd prfrnc (SP) data. Th dsign of th qustionnair should mt prst critria such as inclusion of th statmnt of th study purpos and importanc, clar dfinition of qustions, and avoidanc of prsonal or potntially offnsiv qustions. Th contnts of qustionnair containd (a) pdstrians prsonal profil (ag and gndr), (b) prfrnc for crossing facilitis (crossing location, dtour distanc, and complianc conditions), (c) action principl of crossing choic (i.., which on is considrd to b th first importanc: safty, convninc, saving tim, or saving strngth?), (d) jaywalking conditions (i.., rason and frquncy), and () attitud towards dtour (i.., accptanc lvl and accptabl distanc). Th qustionnair was prtstd bfor ral survy. Thwholsurvyforachpdstrianwasfinishdinral traffic condition and it took lss than 2-3 minuts. Th information about th data collction and corrsponding dfinition of variabls in th survy ar shown in Tabl 1. At th nd of th survy, 402 availabl qustionnairs wr rcivd. Thr wr 205 mal pdstrians and 197 fmal pdstrians participating in th survy. Th most participants wr undr 40 yars of ag. In th fild survy, 1158 pdstrians crossing locations and routs wr rcordd. Thsrcordsalsoincluddthpdstrianswhoparticipatd in th qustionnair survy. From th survy rsults, a majority of pdstrians usd ovrpass/undrpass to cross (46.4% usd ovrpass, 32.7% usd crosswalk, and 20.9% jaywalkd) and most of thm statd that thy prfrrd ovrpass/undrpass in qustionnair (42.1% choos ovrpass and 22.3% choos undrpass). Th rmaining 35.6% prfrrd to cross at pdstrian crosswalk. About th action principl of crossing choic, 50.49% of participants thought of safty as th principl of crossing, 32.17% chos convninc, and 17.32% chos saving tim or physical strngth. Th attitud towards th dtour indicatd that 30.6% of participants wr willingtodtourtousthcrossingfacilityand6.7%of thm rjct to dtour. Th rmaining pdstrians statd thy would accpt dtour in crtain conditions (i.., 37.3% of thm dtour somtim and 25.5% of thm dtour occasionally). Othr rsults showd that most pdstrians (86.13%) could accpt a dtour distanc lss than 100 mtrs. And th rsults indicatd that popl ar willing to dtour in subjctiv dsir but th dtour distanc thy can accpt is short rlativly. Th survy rsults show th pdstrians prfrnc for crossing facilitis. And th SP data ar basically accordant with th RP data so that a conclusion for th survy can b drawn: th survy is availabl. 3. Modl Dmonstration and Estimation 3.1. Modl Dmonstration. According to th stochastic utility thory, th altrnativs hav various utilitis that will influnc th choic. In this papr, thr altrnativs ar considrd, including pdstrian crosswalk, ovrpass (undrpass), and jaywalking. Th ovrpass and undrpass hav th similar physical structur and safguard so thy ar classifid as th sam altrnativ. Jaywalking mans a pdstrian dos
4 Discrt Dynamics in Natur and Socity Variabl Dfinition Not Tabl 1: Dfinition of variabls. X n1 Ag Ag group: (1) 15 23, (2) 24 30, (3) 31 40, (4) 41 55, and (5) >55 X n2 Gndr Pdstrian s gndr: (1) mal and (2) fmal Th principls of strt crossing: (1) safty, (2) convninc, and (3) sav tim or X n3 Principls of crossing strngth X n4 Dtour willingnss a Pdstrian s attitud towards dtour: (1) accpt to dtour, (2) oftn dtour, (3) occasionally dtour, and (4) rfus to dtour X n5 Complianc with th traffic ruls Th dgr of complianc with th traffic ruls: (1) always, (2) oftn, and (3) sldom X n6 Crossing tim Th tim for crossing at crosswalk: (1) pdstrian grn signal, (2) pdstrian rd signal and forc to cross, and (3) pdstrian rd signal and th road is clar X n7 Illgal rason Th rason bhind th illgal crossing: (1) unrasonabl dsign and (2) pdstrians subjctiv rasons X n8 Conformity psychology (1) Pdstrians follow othrs to cross strt (2) Pdstrians do not follow othrs X n9 Dtour distanc Th additional distanc causd by dtour X n10 Travl tim Th tim spnt on crossing strt via crossing facility X n11 Origin and dstination Th origin and dstination of th trip of a pdstrian a Dtour mans a pdstrian has to walk addd distanc to cross th strt at dsignatd location (facility) rathr than to cross dirctly or at th dsird location. Th routs 1 and 2 ar dtour routs as shown in Figur 1. Tabl 2: Modl dmonstration. Variabl Altrnativ Ovrpass/undrpass Crosswalk Jaywalking constant X n1 X n2 X n3 X n4 X n5 X n6 X n7 X n8 X n9 X n10 X n11 not cross th strt using crossing facilitis. Additionally, th modl is basd on th hypothss that th pdstrian himslf is th dcision makr of crossing th strt and h always chooss th satisfactory facilitis. With th altrnativs and xplanatory variabls adoptd abov, utility functions for ach altrnativ can b dfind. Th variabls and componnts of utility functions ar shown in Tabl 2. Whn th absolut valu of t-tst of on xplanatory variabl is gratr than 1.96, this variabl will b considrd that it can influnc th choic with th probability of 95%. If thr is any variabl that cannot influnc th rsult significantly, it will b xcludd and th othr paramtrs will b stimatd again. From initial stimation, th pdstrian s gndr (variabl X n2 ) and pdstrian s complianc with th traffic ruls (variabl X n6 ) ar rjctd. Thn th rmaindr variabls ar stimatd again and th rsults ar shown in Tabl 3. With th rsults, a conclusion can b drawn that th modl is wll bhavd. First, all xplanatory variabls can influnc th choic significantly. Scond, th variabls fit th data wll that th ρ 2 adjustd for th numbr of variabls is 0.396. In contrast, it is common to s an adjustd ρ 2 blow 0.3 in discrt choic modl such as mod choic modls [14]. 3.3. Validating Modl Crdibility. Th stimatd modl is applid with survy data to compar with th actual obsrvations to stablish th crdibility of choic modls and to valuat whthr or not th modl dmonstrats ral bhaviour. Th altrnativ with maximum probability will b chosn. If a calculation rsult is accordant with th survy data, this is dfind as a hit rsult. A hit rsult mans a pdstrian s bhaviour is modld xactly. Lt S in rprsnt th hit rsult that pdstrian n slcts facility i. Considr th following quation: 3.2. Modl Evaluation. With th modl valuation, th paramtrs for th xplanatory variabls ar stimatd in ach utility function by fitting th modls to th obsrvd choic data. Maximum liklihood stimation and t-tst ar adoptd. 1; { if th calculatd rsult is qual to S in = { th survy rsult { 0; othrwis. (4)
Discrt Dynamics in Natur and Socity 5 Tabl 3: Cofficint stimation for xplanatory variabl. Cofficint X n1 X n3 X n4 X n5 X n6 X n7 X n8 X n9 Estimation 0.9112 0.5828 0.906 0.4792 2.341 0.7021 0.014 0.0523 t-tst 2.3632 7.8355 4.3234 2.3632 4.6136 4.2314 2.8926 2.2793 Tabl 4: Hit ratio of MNL modl. Altrnativ Obsrvd rsult Calculation rsult Accordant rsult Hit ratio (%) Crosswalk 131 131 97 74.05% Ovrpass 187 187 154 82.44% Jaywalk 84 84 59 70.23% Total 402 402 310 77.11% Thhitratiocanbcalculatdas 3 R i =, N i i=1 S in 3 i Jm S in R= i=1 3 m=1 J, m whr R i is hit ratio of altrnativ i, R is hit ratio of all altrnativs, N i is th numbr of sampls blonging to altrnativ i,andj m is th numbr of ntir sampls. ThrsultsofthhitratiocanbsninTabl 4. From th rsults in Tabl 4, th hit ratio has indicatd that th modl can xplain th prfrnc of crossing facilitis prfrably. With th proposd modl, th crossing bhaviour canbdiscussdindtail. 4. Discussion of Pdstrian Crossing Bhaviour With th aim of analyzing th crossing bhaviour at various pdstrian facilitis, pdstrians crossing bhaviour is discussd undr spcific hypothtical conditions. Hr, snsitiv analysis is prformd using th proposd modl to illustrat th impact of th considrd variabls, for xampl, action principls, dtour willingnss, and distanc. Ths analyss ar important to undrstand pdstrian bhaviour. 4.1. Effct of Action Principl. Whn pdstrians want to cross th strt, th action principl will influnc th crossing choic significantly. If pdstrians considr safty th first importanc whil crossing strt, thy probably choos crossing facilitis instad of illgal crossing. On th othr hand, if th convninc is considrd th first importanc, jaywalking is asy to happn. This phnomnon is vrifid by th survy data: 41% of th sampls considr safty th first importanc and 39% hav chosn th ovrpass/undrpass. In ordr to study th influnc of th action principl, thr hypothss ar usd: (a) all pdstrians choos safty as action principl, (b) convninc is chosn, and (c) saving tim or physical strngth is chosn. Pdstrians crossing choics ar valuatd by MNL modl and th rsults ar shown in Figur 2. In th rsults of hypothsis (a), (5) Probability 1.0 0.8 0.6 0.4 0.2 0.0 Convninc Jaywalking Crosswalk Ovrpass/undrpass Saving tim Action principls Safty Figur 2: Probability of ach altrnativ with various action principls. th ovrwhlming majority of pdstrians (86.0%) will choos ovrpass/undrpass to cross th strt and only 1.2% of pdstrians will choos crosswalk. Th rsults agr with th truth that ovrpass/ovrpass can provid bttr safguard for pdstrians. Additionally, thr ar still a crtain numbr of jaywalkrs (12.8%) but this is not contrary to th modl: not all pdstrians want to us crossing facilitis. In th rsults of hypothsis (b), convninc is th action principl andthrsultsshowthatalmosthalfofthpdstrians (43.6%) will cross illgally. This is accordant with th currnt situation that jaywalking may b mor convnint than crossing at spcifid facilitis. Somtims, using pdstrian facilitis mans incrasing walking distanc or waiting tim. Pdstrians who choos th crosswalks (31.6%) ar mor than popl who choos th ovrpass/undrpasss (26.8%). Th rsults of hypothsis (b) ar similar to thos of hypothsis (c). Jaywalking may b a propr approach to saving tim or strngth to a crtain dgr, although it is illgal.
6 Discrt Dynamics in Natur and Socity Probability 1.0 0.8 0.6 0.4 0.2 Probability 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Always Oftn Occasionally Rjct Jaywalking Crosswalk Ovrpass/undrpass Dtour willingnss Figur 3: Probability of ach altrnativ with diffrnt dtour willingnss. 4.2. Effct of Dtour Willingnss and Dtour Distanc. In ral traffic condition, pdstrians may dtour to arriv at th location with crossing facilitis rathr than crossing anywhr or anytim thy want. Such dtour incras crossing distanc and influnc crossing bhaviour significantly. Thrfor, it is important for nginrs to dsign crossing facilitis with rasonabl intrval distanc. Hr, pdstrians attituds about th dtour and accptabl dtour distanc ar considrd. According to th qustionnair survy, pdstrians attituds towards th dtour ar valuatd by th frquncy of dtour, which is dividd into four lvls: always accpt, oftn, occasionally, and rjct. Hr th crossing bhaviour is rprsntd undr assumd conditions if all of th pdstrians slct th sam attitud to cross th strt. From th rsults, as shown in Figur 3, with dcras of th accptanc frquncy, th probability that th ovrpass/undrpass is chosn is in a downtrnd. In contrast, th probabilitis that th crosswalk or jaywalking is chosn incrass and th probability of jaywalking would incras vn fastr. Ths rsults ar accordant with th rality that jaywalking is a dirct and convnint way if pdstrians ar not willing to dtour to us th crossing facilitis. Furthrmor, th survy data also confirm th rsult (only 30.6% of th participants can accpt dtour and narly half of thm sldom dtour). On th othr hand, th accptabl distanc for dtouring is important to xplain th crossing bhaviour that popl cannot cross at th xpctd location. Pdstrians attituds towards dtour would rflct thir prsonal dsir, but th dtour distanc may chang th final choic. Th survy data prsnt th fact that majority of participants (86.13%) arwillingtoaccptthdtourdistancwithin100mtrs. It mans, if th dtour distanc is longr than 100 mtrs, pdstrians may chang thir mind vn jaywalk. With th hlp of MNL modl, th snsitivity about dtour distanc is analyzd. As shown in Figur 4, it is clar that th dtour distanc can influnc th probability of jaywalking. 0.0 0 20 40 60 80 100 120 140 160 180 200 Dtour distanc (m) Crossovr Ovrpass/undrpass Jaywalking Figur 4: Probability of ach altrnativ with diffrnt accptabl dtour distanc. Thrsultsshowthatonly2.74%ofpoplwillcrossillgally on th prmis that accptabl distanc is 200 mtrs. On th contrary, 43.5% of pdstrians may jaywalk if such distanc is shortr than 50 mtrs. Hr, a paramtr namd complianc indx (CI) is dfind as th diffrnc that th probability of lgal crossing minus jaywalking probability. This paramtr indicats th lvl to which pdstrians comply with traffic rgulations whn thy ar in conditions of various dtour distancs. So largr CI paramtr mans only a fw pdstrians violat th traffic rgulations. As shown in Figur 5, thcicurv dcrass with th incras of dtour distanc. A rapid dcras appars btwn 75 and 150 mtrs. This trnd is accordant with th survy rsults and it is usful to giv som suggstions for dsign of pdstrian facilitis. According to th curv fitting, th function of CI is givn by D i (S) =α tanh ( s γ)+β, (6) φ whr D i (S) is function of CI at location i and S is dtour distanc to gt location i. ThCIcurvisshownasablulinandthfittingcurv of (6) (withα = 0.38, β = 0.45, φ = 46.66, andγ = 2.45) isshownasardlininfigur 5. AsshowninFigur 5, (6) has a fair goodnss of fit and it can prsnt th faturs of CI curv. 4.3. Walk First or Cross First. Th abov discussions about dtour focus on th scn that th dstination is opposit to th origin. On th othr hand, th dstination is on th othr sid of th strt diagonally and thr ar svral crossing facilitis locatd btwn thm. In this scn, pdstrians would considr whthr cross first or walk first. For xampl, thoriginisinzon1andthdstinationisinzon6(as shown in Figur 1), thr ar two choics: to cross first via
Discrt Dynamics in Natur and Socity 7 Probability 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 Dtour distanc (m) Complianc crossing Jaywalking CI curv Fitting curv Figur 5: Illustration of complianc indx. th crosswalk or walk first thn cross via th ovrpass. On th basis of th survy, th probabilitis of th abov qustions ar givn by th following. Cross first and walk latr: P c = 0.632. Walk first and cross latr: P w = 0.368. This mans pdstrians ar inclind to cross arlir. Th rsult can b xplaind by th fact that popl may miss a propr crossing location if thy kp going. Espcially for popl who ar not familiar with th locations of crossing facilitis, thy ar willing to cross at first whn thy gt a cross facility. Yannis t al. [15] obtaindasimilarrsultand gav a linar formula of probability distribution to dscrib th cross first bhaviour. In th rsarch of Yannis t al., a pdstrian s trip may includ svral blocks, so popl may hav divrs choics such as midblock or intrsction. But it is not ncssary for pdstrians to walk so long distanc in most ral conditions. Whil walking along th trip, pdstrians who ar familiar with th traffic nvironmnt can choos th cross locations thy prfr. Howvr, th strangrs ar inclind to us th first facility thy gt. This phnomnon givs a mssag that crossing facilitis should b nar th gnrating/attracting sourc of walk trip. 5. Applications and Enginring Improvmnts Accordingtothanalysisofpdstrianbhaviour,itisknown that pdstrians subjctiv willingnss can dtrmin th final choic of crossing location. Th influntial factors lad to divrs choics in th sam circumstanc: som pdstrians prfr th crossing facilitis, but som cross illgally. This is bcaus pdstrians thmslvs ar vry appropriat to idntify whthr th traffic nvironmnts ar dsirabl. Rasonabl dsigning and opration of crossing facilitis which match pdstrians charactristics can conduct th pdstrians bhaviour and incras th us of pdstrian facilitis. So th rquirmnts in dsigning of crossing facilitis ar to satisfy pdstrian nds and improv pdstrian safty and comfort. Hr, som nginring improvmnts ar discussd basd on pdstrians bhavioural charactristics in ordr to mak contribution to th traffic nvironmnts. (a) Grad-sparatd crossing facilitis ar rcommndd for pdstrian safty and traffic prformanc. Though ths facilitis ar built undr svr construction conditions, pdstrian ovrpass or undrpass is th bst choic, spcially in businss quartrs and rsidntial aras. (b) In th sight of pdstrian, th shortr intrval distanc is mor convnint. Considring th rquirmnts of prformanc and fairnss, th commndatory intrval distanc btwn two crossing facilitis is 300 mtrs (400 mtrs at th most). This is bcaus a shortrintrvalwillincrastrafficdlayanddcras th utility rat of facilitis. On th contrary, th long intrval may incras pdstrian violation. (c)thconsidrationaboutthlocationandtypof crossing facilitis is vry important. Pdstrians bhavioural charactristics should b considrd sriously,aswllasthlandusaroundthstrt.th main gnrating/attracting sourcs of walk trip (.g., school and shopping mall) should b concrnd spcially. In othr words, crossing facilitis mainly srv such trip sourcs. (d) In rspons to th situation whr pdstrian nds to dtour, th stratgy is th narr th bttr. If th dtour distanc is invitabl, such distanc is rcommndd to b lss than 150 mtrs. This schm aims to rduc th possibility of jaywalking and it is important for th ara with larg pdstrian flow. () If thr ar trip gnrating/attracting sourcs at both sid of th strt diagonally, pdstrians will fac th altrnativs whthr cross first or walk first. According to abov discussion, pdstrians ar inclind to cross first and walk latr. Thrfor it will b bttr to st up two facilitis for ach sourc if th intrval is mor than 200 mtrs. On th othr hand, if th intrval is shortr than 200 mtrs, it will b bttr to dsign a facility in th middl of thm. Finally, to strngthn th awarnss of traffic safty is th most basic and th most fficint masur to minimiz pdstrian violation. 6. Conclusions This papr xamins th pdstrians prfrncs of crossing locations and th influntial factors in making a dcision to cross a strt. Information is obtaind through qustionnair survyandfildobsrvationinbijing.amultinomiallogit modl is usd to dscrib th crossing bhaviour undr various traffic conditions. And how th influntial factors hav impact on th crossing action is rvald by snsitivity analysis. Th following conclusions ar drawn basd upon th rsults.
8 Discrt Dynamics in Natur and Socity (a) Thr is a rlativly good agrmnt btwn th information of qustionnair and pdstrian actual bhaviour in trms of thir crossing choics. Th MNL modl can dscrib crossing bhaviour prfrably. (b)thmostinfluntialsubjctivfactorinmakinga dcision to cross at a dsignatd crossing location is th action principl (variabl X n3 ). Th most influntial factor in xtrnal nvironmnt is th dtour distanc (variabl X n9 ). (c) A rasonabl dsigning and a propr opration of crossing facilitis can conduct crossing bhaviour and incras th utilization rat of facilitis. Pdstrians thmslvs ar th most appropriat group to idntify th rationality and srvicability of pdstrian nvironmnt. (d) Th rsults indicat that pdstrians prfr ovrpass/undrpass, and most pdstrians considr safty th first importanc. In a viw of cost and construction conditions, signalizd crosswalk is rcommndd to hlp minimiz th pdstrian-vhicl conflicts. Th findings from this papr ar xpctd to hlp undrstand pdstrians bhaviour at crossing locations wll. Though pdstrians prfrncs and th rasons bhind th choicarxplaindbyadiscrtchoicmodl,thrarstill som insufficincis in th work. For xampl, som potntial influntial factors may b nglctd or th factor s influncing dgr is waknd so that th modl cannot rflct th ffcts of variabls comprhnsivly. Additionally, aggrgat rsults for crossing bhaviour with various OD pairs and th rason for pdstrian violation should b considrd furthr. Conflict of Intrsts Th authors dclar that thr is no conflict of intrsts rgarding th publication of this papr. Acknowldgmnts This rsarch was supportd in part by th National Natur Scinc Foundation of China undr Grants 51378062 and 71301010 and th Introducing Talnts of Disciplin to Univrsitis undr Grant B12022. Rfrncs [4] W.H.K.Lam,J.Y.S.L,andC.Y.Chung, Astudyofth bi-dirctional pdstrian flow charactristics at Hong Kong signalizd crosswalk facilitis, Transportation,vol.29,no.2,pp. 169 192, 2002. [5] V. P. Sisiopiku and D. Akin, Pdstrian bhaviors at and prcptions towards various pdstrian facilitis: an xamination basdonobsrvationandsurvydata, Transportation Rsarch F: Traffic Psychology and Bhaviour, vol.6,no.4,pp.249 274, 2003. [6] S. Sarkar, Evaluation of safty for pdstrians at macro- and microlvls in urban aras, Transportation Rsarch Rcord, no. 1502, pp. 105 118, 1995. [7]J.Y.S.L,P.K.Goh,andW.H.K.Lam, Nwlvl-ofsrvic standard for signalizd crosswalks with bi-dirctional pdstrian flows, Transportation Enginring,vol.131, no. 12, pp. 957 960, 2005. [8] R. Elvik, M. W. J. Sørnsn, and T.-O. Nævstad, Factors influncing safty in a sampl of markd pdstrian crossings slctd for safty inspctions in th city of Oslo, Accidnt Analysis and Prvntion,vol.59,pp.64 70,2013. [9] K. Shrivr, Influnc of nvironmntal dsign on pdstrian travl bhavior in four Austin nighborhoods, Transportation Rsarch Rcord, no. 1578, pp. 64 75, 1997. [10] B. Li, A modl of pdstrians intndd waiting tims for strt crossings at signalizd intrsctions, Transportation Rsarch B: Mthodological,vol.51,pp.17 28,2013. [11] P. Lambrianidou, S. Basbas, and I. Politis, Can pdstrians crossing countdown signal timrs promot grn and saf mobility? Sustainabl Citis and Socity, vol. 6, pp. 33 39, 2013. [12] H.Guo,W.Wang,W.Guo,X.Jiang,andH.Bubb, Rliability analysis of pdstrian safty crossing in urban traffic nvironmnt, Safty Scinc, vol. 50, no. 4, pp. 968 973, 2012. [13] H.Guo,Z.Gao,X.Yang,andX.Jiang, Modlingpdstrian violation bhavior at signalizd crosswalks in China: a hazardsbasd duration approach, Traffic Injury Prvntion,vol.12,no. 1, pp. 96 103, 2011. [14] X. Chu, M. Guttnplan, and M. R. Balts, Why popl cross whrthydo:throlofstrtnvironmnt, Transportation Rsarch Rcord, no. 1878, pp. 3 10, 2003. [15] G. Yannis, J. Golias, and E. Papadimitriou, Modling crossing bhavior and accidnt risk of pdstrians, Transportation Enginring,vol.133,no.11,pp.634 644,2007. [16] H. Nassiri and Y. Sajd, Using a logit modl to prdict pdstrian crossing bhaviour basd upon vhicl spd and hadway on multi-lan strt, in Procdings of th 88th Annual Mting of th Transportation Rsarch Board, Washington DC, USA, 2009. [17] M. Bn-Akiva and L. Stvn, Discrt Choic Analysis: Thory and Application to Travl Dmand, MIT Prss, Cambridg, Mass, USA, 1985. [1] M. Huan, X. B. Yang, and B. Jia, Crossing rliability of lctric bik ridrs at urban intrsctions, Mathmatical Problms in Enginring,vol.2013,ArticlID108636,8pags,2013. [2] J. J. Fruin, Pdstrian Planning and Dsign, Mtropolitan Association of Urban Dsignrs and Environmntal Plannrs, Nw York, NY, USA, 1971. [3] S. T. Mohammd, Evaluation of pdstrian spd in Jordan with invstigation of som contributing factors, Safty Rsarch,vol.32,no.2,pp.229 236,2001.
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